Construction of New D=3, N=4 Quiver Gauge Theories

TL;DR

This paper introduces a new class of 3-algebras called double-symplectic 3-algebras and constructs D=3, N=4 quiver gauge theories systematically using these algebraic structures, providing new examples and re-deriving known theories.

Contribution

It proposes a systematic construction method for D=3, N=4 quiver gauge theories using double-symplectic 3-algebras and superalgebras, including new gauge groups and re-derivation of existing theories.

Findings

Introduced double-symplectic 3-algebras and their contraction to N=4 three-algebras.

Constructed explicit examples of new gauge groups in D=3, N=4 theories.

Re-derived general N=4 superconformal Chern-Simons theories using the new 3-algebra approach.

Abstract

In this paper we propose a special class of 3-algebras, called double-symplectic 3-algebras. We further show that a consistent contraction of the double-symplectic 3-algebra gives a new 3-algebra, called an N=4 three-algebra, which is then identified as the exact gauged three-algebra in the N=4 quiver gauge theories. A systematic construction is proposed for the 3-brackets and fundamental identities used in building up the N=4 theories, by starting with two superalgebras whose bosonic parts share at least one simple factor or U(1) factor. This leads to a systematic way of constructing D=3, N=4 quiver theories, of which several examples with new gauge groups are presented in detail. The general N=4 superconformal Chern-Simons matter theories in terms of ordinary Lie algebras can be also re-derived in our new 3-algebra approach.